Mechanical arm tail end safety control method and system for cultural relic fingerprints

Abstract

The invention provides a mechanical arm tail end safety control method and system for cultural relic fingerprints, and belongs to the technical field of robot control. Aiming at a mechanical arm tail end trajectory tracking control task on a cultural relic surface, firstly, a kinematic model and a dynamic model of a mechanical arm are established; secondly, designing a self-adaptive control algorithm based on a kinematics model and a dynamics model, and solving the problem of uncertainty of kinematics and dynamics parameters of the mechanical arm without solving inertia matrix inverse and measuring angular acceleration; and finally, deducing a globally asymptotically stable trajectory tracking control law, obtaining a driving torque instruction of a mechanical arm joint, ensuring that the tail end of the mechanical arm carries an optical probe to stably track the expected trajectory of the surface of the cultural relic, and ensuring that the mechanical arm completes the task of tracking the trajectory of fingerprint extraction and identification of the cultural relic under a complex working condition.

Description

Technical Field

[0001] The present invention relates to the field of robot control technology, and in particular to a method and system for controlling the safety of a robotic arm end facing cultural relic fingerprints. Background Art

[0002] In the field of cultural relic protection, accurately identifying cultural relics and monitoring changes in their condition are crucial. As an emerging and effective method, cultural relic fingerprint extraction and identification technology is gradually gaining widespread attention.

[0003] In the fingerprint extraction and identification process for cultural relics, robotic arms, as devices capable of automated operation, have significant application potential. They can carry equipment such as microscopic probe cameras to precisely locate, focus, and collect information about cultural relics. However, existing robotic arms face numerous challenges when applied to fingerprint extraction and identification of museum artifacts. For one thing, traditional robotic arm trajectory tracking control methods, such as pre-programmed grasping, can only execute tasks in fixed scenarios according to pre-set trajectories and motion sequences. They lack adaptability to variations in the shape, size, and placement of cultural relics. Any changes in the placement environment or the state of the cultural relics themselves require complex reprogramming and configuration, which is both time-consuming and labor-intensive in practical cultural relic conservation work and fails to meet the requirements of efficient and accurate work. Furthermore, while vision-guided grasping utilizes visual sensors to acquire object information and implement grasp planning, it places extremely high demands on visual recognition. Cultural relics often have complex shapes and diverse materials, and some are transparent or reflective. Furthermore, in museum environments, the backgrounds are complex. These factors make it difficult for existing vision-guided grasping methods to accurately locate cultural relics, thus affecting the accuracy and reliability of fingerprint extraction.

[0004] Furthermore, due to the extremely high historical, cultural, and artistic value of cultural relics, fingerprint extraction and identification operations place extremely stringent demands on the end-user tracking accuracy and stability of the robotic arm. Any slight deviation could damage the artifact or prevent accurate fingerprint information from being captured. However, current robotic arm control technology struggles to achieve high-precision, stable, adaptive end-user tracking in complex cultural relic protection scenarios. Summary of the Invention

[0005] In order to solve the problems in the above-mentioned prior art, the present invention provides a method and system for safe control of the end of a manipulator for cultural relic fingerprints. The invention is aimed at the task of tracking the trajectory of the end of the manipulator on the surface of the cultural relic. First, a kinematic model and a dynamic model of the manipulator are established to deal with the uncertainty of the model; secondly, an adaptive control algorithm based on the kinematic model and the dynamic model is designed, which eliminates the need to solve the inverse of the inertia matrix and measure the angular acceleration and solves the uncertainty problem of the kinematic and dynamic parameters of the manipulator; finally, a globally asymptotically stable trajectory tracking control law is derived to obtain the driving torque command of the manipulator joint, ensuring that the end of the manipulator carries an optical probe to stably track the desired trajectory of the cultural relic surface, and ensuring that the manipulator completes the task of tracking the trajectory of cultural relic fingerprint extraction and identification under complex working conditions. To achieve the above purpose, the technical solution is as follows:

[0006] In one aspect, the present invention provides a method for controlling the safety of a robotic arm end for cultural relic fingerprints, the method comprising:

[0007] S1. Obtain the expected motion trajectory and expected motion speed based on the cultural relic fingerprint;

[0008] S2. According to the robotic arm, by measuring the end trajectory of the robotic arm, obtain the real-time motion trajectory and real-time motion speed of the end of the robotic arm;

[0009] S3, according to the real-time motion trajectory and the real-time motion speed of the end of the robotic arm, obtaining the actual trajectory and the actual speed of the robotic arm joint;

[0010] S4. Obtaining a tracking error of the end of the robotic arm according to the expected motion trajectory and the real-time motion trajectory of the end of the robotic arm;

[0011] S5. Obtain estimated values of a reference trajectory of the manipulator joint, a reference velocity of the manipulator joint, and a Jacobian matrix of the manipulator through a kinematic model based on the expected motion trajectory, the expected motion velocity, the real-time motion trajectory of the manipulator end, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, and the tracking error of the manipulator end;

[0012] S6. Obtaining a tracking error of the robotic arm joint according to the reference speed of the robotic arm joint and the actual speed of the robotic arm joint;

[0013] S7. Obtaining an adaptive update law for an estimated value of an inertial parameter vector according to the tracking error of the manipulator joint;

[0014] S8. Obtaining a driving torque command for the manipulator joint through a dynamic model according to the manipulator joint reference velocity, the estimated value of the manipulator Jacobian matrix, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the tracking error of the manipulator end, and the estimated value of the inertia parameter vector, using an adaptive update law;

[0015] S9. Control the joints of the robotic arm according to the driving torque instructions of the joints of the robotic arm to obtain the final end motion trajectory of the robotic arm.

[0016] Optionally, in S4, obtaining the tracking error of the end of the manipulator according to the expected motion trajectory and the real-time motion trajectory of the end of the manipulator includes: obtaining the tracking error of the end of the manipulator by formula (1),

[0017] e x =X c (t)-X(t) (1)

[0018] Where: e x is the tracking error of the end of the robot arm, X c (t) is the expected motion trajectory, and X(t) is the real-time motion trajectory of the end of the robotic arm.

[0019] Optionally, in S5, according to the expected motion trajectory, the expected motion speed, the real-time motion trajectory of the end of the manipulator, the actual trajectory of the manipulator joint, the actual speed of the manipulator joint, and the tracking error of the end of the manipulator, obtaining the estimated values of the manipulator joint reference trajectory, the manipulator joint reference speed, and the manipulator Jacobian matrix through the kinematic model includes:

[0020] S51. According to the tracking error of the end of the manipulator, the adaptive update law of the kinematic parameter vector estimation value is obtained through formula (2):

[0021]

[0022] Where: is the adaptive update law for the estimated value of the kinematic parameter vector, K B is the first positive definite gain matrix, Y K is the first linear regression matrix, q r is the reference trajectory of the robot arm joint, is the reference speed of the robot joint, K p is the second positive definite gain matrix, e x is the tracking error of the end of the robotic arm;

[0023] S52, according to the actual trajectory of the manipulator joint, the actual speed of the manipulator joint and the adaptive update law of the estimated value of the kinematic parameter vector, obtain the estimated value of the manipulator Jacobian matrix through formula (3),

[0024]

[0025] Where: is the estimated value of the Jacobian matrix of the robot arm, q is the actual trajectory of the robot arm joint, is the actual speed of the robot arm joint;

[0026] S53, according to the expected motion trajectory, the expected motion speed, the real-time motion trajectory of the end of the manipulator and the estimated value of the Jacobian matrix of the manipulator, the manipulator joint reference speed is obtained by formula (4),

[0027]

[0028] Where: K v is the third positive definite gain matrix, X c (t) is the expected motion trajectory, X(t) is the real-time motion trajectory of the end of the robot arm, is the expected movement speed;

[0029] S54: Obtain a reference trajectory of the arm joint by integrating the reference velocity of the arm joint.

[0030] Optionally, in S6, obtaining the tracking error of the manipulator joint according to the manipulator joint reference speed and the actual speed of the manipulator joint includes: obtaining the tracking error of the manipulator joint by formula (5),

[0031]

[0032] Where: r is the tracking error of the robot arm joint, is the reference speed of the robot joint, is the actual velocity of the robot arm joint.

[0033] Optionally, in S7, an adaptive update law for the estimated value of the inertial parameter vector is obtained according to the tracking error of the manipulator joint, including: obtaining an adaptive update law for the estimated value of the inertial parameter vector by formula (6),

[0034]

[0035] Where: is the adaptive update law of the estimated inertial parameter vector, K A is the fourth positive definite gain matrix, Y is the second linear regression matrix, and r is the tracking error of the robotic arm joint.

[0036] Optionally, in S8, obtaining a driving torque command of the manipulator joint according to the manipulator joint reference velocity, the estimated value of the manipulator Jacobian matrix, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the tracking error of the manipulator end, and the estimated value of the inertia parameter vector through a dynamic model includes:

[0037] S81. Obtain an estimated value of a reference acceleration of the manipulator joint by taking a derivative based on the manipulator joint reference velocity.

[0038] S82, obtaining an estimated value of the inertia parameter vector by integration according to an adaptive update law of the estimated value of the inertia parameter vector;

[0039] S83, according to the estimated value of the reference acceleration of the manipulator joint, the reference velocity of the manipulator joint, the estimated value of the Jacobian matrix of the manipulator, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the real-time motion trajectory of the manipulator end and the estimated value of the inertia parameter vector, obtain the driving torque instruction of the manipulator joint through formula (7),

[0040]

[0041] Where: τ is the driving torque command of the manipulator joint, Y is the second linear regression matrix, q is the actual trajectory of the manipulator joint, is the actual speed of the robot arm joint, is the reference speed of the robot joint, is the estimated value of the reference acceleration of the manipulator joint, is the estimated value of the inertial parameter vector, K d is the fifth positive definite gain matrix, r is the tracking error of the manipulator joint, is the estimated value of the Jacobian matrix of the robot arm, K p is the second positive definite gain matrix, e x is the tracking error of the end of the robotic arm, is the upper bound of interference, and sign() is the sign function.

[0042] On the other hand, the present invention provides a robot arm end safety control system for cultural relic fingerprints, which is applied to a robot arm end safety control method for cultural relic fingerprints. The system includes:

[0043] The first acquisition module is used to obtain the expected motion trajectory and expected motion speed according to the cultural relic fingerprint;

[0044] A second acquisition module is configured to obtain a real-time motion trajectory and a real-time motion speed of the end of the robotic arm by measuring the end trajectory of the robotic arm according to the robotic arm;

[0045] A first calculation module is used to obtain an actual trajectory and an actual speed of the robotic arm joint according to the real-time motion trajectory and the real-time motion speed of the robotic arm end;

[0046] A second calculation module is used to obtain a tracking error of the end of the robotic arm according to the expected motion trajectory and the real-time motion trajectory of the end of the robotic arm;

[0047] a kinematic control module, configured to obtain, through a kinematic model, an estimated value of a reference trajectory of the manipulator joint, a reference velocity of the manipulator joint, and a Jacobian matrix of the manipulator according to the desired motion trajectory, the desired motion velocity, the real-time motion trajectory of the manipulator end, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, and the tracking error of the manipulator end;

[0048] a third calculation module, configured to obtain a tracking error of the manipulator joint according to a reference speed of the manipulator joint and an actual speed of the manipulator joint;

[0049] a fourth calculation module, configured to obtain an adaptive update law for an estimated value of an inertial parameter vector according to a tracking error of the joint of the manipulator;

[0050] a dynamics control module, configured to obtain a driving torque command for the joint of the manipulator arm through a dynamics model based on a reference velocity of the joint of the manipulator arm, an estimated value of the Jacobian matrix of the manipulator arm, an actual trajectory of the joint of the manipulator arm, an actual velocity of the joint of the manipulator arm, a tracking error of the joint of the manipulator arm, a tracking error of the end of the manipulator arm, and an adaptive update law of an estimated value of the inertial parameter vector;

[0051] The trajectory output module is used to control the joints of the robotic arm according to the driving torque instructions of the robotic arm joints to obtain the final end motion trajectory of the robotic arm.

[0052] Compared with the prior art, the technical solution of the present invention has at least the following beneficial effects:

[0053] On the one hand, the above scheme establishes the kinematic model and dynamic model of the robotic arm to deal with the uncertainty of the model; on the other hand, it designs an adaptive control algorithm based on the kinematic model and the dynamic model, which eliminates the need to solve the inverse of the inertia matrix and measure the angular acceleration and solves the uncertainty problem of the kinematic and dynamic parameters of the robotic arm; on the third hand, it derives a globally asymptotically stable trajectory tracking control law and obtains the driving torque command of the robotic arm joint, ensuring that the optical probe carried by the end of the robotic arm stably tracks the desired trajectory of the cultural relic surface, ensuring that the robotic arm can complete the task of tracking the trajectory for fingerprint extraction and identification of cultural relics under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0055] Figure 1 This is a flow chart of an embodiment of the method for controlling the safety of a robotic arm end for cultural relic fingerprints according to the present invention;

[0056] Figure 2 1 is a schematic diagram of a scenario in which a robotic arm tracks a collection fingerprint in an embodiment of a robotic arm terminal security control method for cultural relics fingerprints of the present invention;

[0057] Figure 3 is a graph of the expected trajectory and the actual trajectory of the robotic arm end in an embodiment of the robotic arm end safety control method for cultural relic fingerprints of the present invention;

[0058] Figure 4 is a graph showing the change in tracking error of the end of a robotic arm over time in an embodiment of the method for controlling the end of a robotic arm for cultural relics fingerprints of the present invention;

[0059] Figure 5 is a graph showing the change in tracking error of a robotic arm joint over time in an embodiment of the robotic arm end safety control method for cultural relic fingerprints of the present invention;

[0060] Figure 6 is a graph showing the real-time motion trajectory of the end of the manipulator and the final end motion trajectory of the manipulator in consideration of parameter perturbation in an embodiment of the manipulator end safety control method for cultural relics fingerprints of the present invention;

[0061] Figure 7 is a graph showing the real-time motion trajectory of the end of the manipulator and the final end motion trajectory of the manipulator without interference suppression in an embodiment of the manipulator end security control method for cultural relics fingerprints of the present invention;

[0062] Figure 8 is a graph showing the change in tracking error of the end of the manipulator over time in the absence of interference suppression in an embodiment of the manipulator end safety control method for cultural relic fingerprints of the present invention;

[0063] Figure 9 A graph showing the real-time motion trajectory of the end of the robotic arm and the final end motion trajectory of the robotic arm in the case of interference suppression in an embodiment of the robotic arm end safety control method for cultural relics fingerprints of the present invention;

[0064] Figure 10 is a graph showing the change in tracking error of the end of the manipulator over time in the case of interference suppression in an embodiment of the manipulator end safety control method for cultural relic fingerprints of the present invention;

[0065] Figure 11 is a graph showing the change in tracking error of a robotic arm joint over time in the embodiment of the robotic arm end safety control method for cultural relic fingerprints of the present invention with interference suppression;

[0066] Figure 12 It is a curve diagram of a square trajectory tracked by a robotic arm end in an embodiment of the robotic arm end safety control method for cultural relic fingerprints of the present invention;

[0067] Figure 13 This is a graph showing the change in tracking error of the robotic arm joint over time when the robotic arm end tracks a square trajectory in an embodiment of the robotic arm end safety control method for cultural relic fingerprints of the present invention;

[0068] Figure 14 1 is a graph showing a smoothed square trajectory of a robotic arm end in accordance with an embodiment of a robotic arm end safety control method for cultural relic fingerprints of the present invention;

[0069] Figure 15 This is a graph showing the change in tracking error of the robot arm joint over time when the robot arm end tracks a smoothed square trajectory in an embodiment of the robot arm end safety control method for cultural relic fingerprints of the present invention;

[0070] Figure 16 It is a curve diagram of the end of the robotic arm tracking the Archimedean spiral trajectory in an embodiment of the robotic arm end security control method for cultural relics fingerprints of the present invention;

[0071] Figure 17 It is a flow chart of obtaining estimated values of a manipulator arm joint reference trajectory, a manipulator arm joint reference velocity, and a manipulator arm Jacobian matrix in an embodiment of the manipulator arm end safety control method for cultural relic fingerprints of the present invention;

[0072] Figure 18This is a flow chart of obtaining a driving torque instruction for a robotic arm joint in an embodiment of the robotic arm end safety control method for cultural relic fingerprints of the present invention;

[0073] Figure 19 This is a system block diagram of an embodiment of a robotic arm end safety control system for cultural relic fingerprints of the present invention. DETAILED DESCRIPTION

[0074] The technical solution of the present invention is described below in conjunction with the accompanying drawings.

[0075] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as an "exemplary" in the present invention should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of the word "exemplary" is intended to present concepts in a concrete manner. Furthermore, in the embodiments of the present invention, "and / or" can mean both or either of the two.

[0076] In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0077] like Figure 1 The flowchart of the embodiment of the robot arm end security control method for cultural relics fingerprint of the present invention is shown as follows Figure 2 The schematic diagram of a scenario in which a robotic arm tracks a collection fingerprint in an embodiment of a robotic arm terminal security control method for cultural relic fingerprints of the present invention is shown. The present invention provides a robotic arm terminal security control method for cultural relic fingerprints. The method is implemented by a robotic arm terminal security control system for cultural relic fingerprints. The method includes:

[0078] S1. Obtain the expected motion trajectory and expected motion speed based on the cultural relic fingerprint;

[0079] S2. According to the robotic arm, by measuring the end trajectory of the robotic arm, obtain the real-time motion trajectory and real-time motion speed of the end of the robotic arm;

[0080] S3, according to the real-time motion trajectory and the real-time motion speed of the end of the robotic arm, obtaining the actual trajectory and the actual speed of the robotic arm joint;

[0081] S4. Obtaining a tracking error of the end of the robotic arm according to the expected motion trajectory and the real-time motion trajectory of the end of the robotic arm;

[0082] Specifically, in S4, the tracking error of the end of the manipulator is obtained according to the expected motion trajectory and the real-time motion trajectory of the end of the manipulator, including: obtaining the tracking error of the end of the manipulator through formula (1),

[0083] e x =X c (t)-X(t) (1)

[0084] Where: e x is the tracking error of the end of the robot arm, X c (t) is the expected motion trajectory, and X(t) is the real-time motion trajectory of the end of the robotic arm.

[0085] S5. Obtain estimated values of a reference trajectory of the manipulator joint, a reference velocity of the manipulator joint, and a Jacobian matrix of the manipulator through a kinematic model based on the expected motion trajectory, the expected motion velocity, the real-time motion trajectory of the manipulator end, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, and the tracking error of the manipulator end;

[0086] Specifically, if Figure 17 The flowchart of obtaining the estimated values of the manipulator joint reference trajectory, the manipulator joint reference velocity, and the manipulator Jacobian matrix in the embodiment of the manipulator end terminal security control method for cultural relic fingerprints of the present invention is shown. In S5, the estimated values of the manipulator joint reference trajectory, the manipulator joint reference velocity, and the manipulator Jacobian matrix are obtained through the kinematic model based on the expected motion trajectory, the expected motion velocity, the real-time motion trajectory of the manipulator end terminal, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, and the tracking error of the manipulator end terminal, including:

[0087] S51. According to the tracking error of the end of the manipulator, the adaptive update law of the kinematic parameter vector estimation value is obtained through formula (2):

[0088]

[0089] Where: is the adaptive update law for the estimated value of the kinematic parameter vector, K B is the first positive definite gain matrix, Y K is the first linear regression matrix, q r is the reference trajectory of the robot arm joint, is the reference speed of the robot joint, K p is the second positive definite gain matrix, e x is the tracking error of the end of the robotic arm;

[0090] S52, according to the actual trajectory of the manipulator joint, the actual speed of the manipulator joint and the adaptive update law of the estimated value of the kinematic parameter vector, obtain the estimated value of the manipulator Jacobian matrix through formula (3),

[0091]

[0092] Where: is the estimated value of the Jacobian matrix of the robot arm, q is the actual trajectory of the robot arm joint, is the actual speed of the robot arm joint;

[0093] S53, according to the expected motion trajectory, the expected motion speed, the real-time motion trajectory of the end of the manipulator and the estimated value of the Jacobian matrix of the manipulator, the manipulator joint reference speed is obtained by formula (4),

[0094]

[0095] Where: K v is the third positive definite gain matrix, X c (t) is the expected motion trajectory, X(t) is the real-time motion trajectory of the end of the robot arm, is the expected movement speed;

[0096] S54: Obtain a reference trajectory of the arm joint by integrating the reference velocity of the arm joint.

[0097] S6. Obtaining a tracking error of the robotic arm joint according to the reference speed of the robotic arm joint and the actual speed of the robotic arm joint;

[0098] Specifically, in S6, the tracking error of the manipulator joint is obtained according to the reference speed of the manipulator joint and the actual speed of the manipulator joint, including: obtaining the tracking error of the manipulator joint through formula (5),

[0099]

[0100] Where: r is the tracking error of the robot arm joint, is the reference speed of the robot joint, is the actual velocity of the robot arm joint.

[0101] S7. Obtaining an adaptive update law for an estimated value of an inertial parameter vector according to the tracking error of the manipulator joint;

[0102] Specifically, in S7, the adaptive update law of the estimated value of the inertial parameter vector is obtained according to the tracking error of the manipulator joint, including: obtaining the adaptive update law of the estimated value of the inertial parameter vector through formula (6),

[0103]

[0104] Where: is the adaptive update law of the estimated inertial parameter vector, K A is the fourth positive definite gain matrix, Y is the second linear regression matrix, and r is the tracking error of the robotic arm joint.

[0105] S8. Obtaining a driving torque command for the manipulator joint through a dynamic model according to the manipulator joint reference velocity, the estimated value of the manipulator Jacobian matrix, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the tracking error of the manipulator end, and the estimated value of the inertia parameter vector, using an adaptive update law;

[0106] Specifically, if Figure 18 The flowchart of the embodiment of the method for controlling the terminal end of a manipulator for cultural relic fingerprints of the present invention for obtaining the driving torque instruction of the manipulator joint is shown. In step S8, the driving torque instruction of the manipulator joint is obtained through a dynamic model based on the reference velocity of the manipulator joint, the estimated value of the manipulator Jacobian matrix, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the tracking error of the terminal end of the manipulator, and the adaptive update law of the estimated value of the inertia parameter vector, including:

[0107] S81. Obtain an estimated value of a reference acceleration of the manipulator joint by taking a derivative based on the manipulator joint reference velocity.

[0108] S82, obtaining an estimated value of the inertia parameter vector by integration according to an adaptive update law of the estimated value of the inertia parameter vector;

[0109] S83, according to the estimated value of the reference acceleration of the manipulator joint, the reference velocity of the manipulator joint, the estimated value of the Jacobian matrix of the manipulator, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the real-time motion trajectory of the manipulator end and the estimated value of the inertia parameter vector, obtain the driving torque instruction of the manipulator joint through formula (7),

[0110]

[0111] Where: τ is the driving torque command of the manipulator joint, Y is the second linear regression matrix, q is the actual trajectory of the manipulator joint, is the actual speed of the robot arm joint, is the reference speed of the robot joint, is the estimated value of the reference acceleration of the manipulator joint, is the estimated value of the inertial parameter vector, K d is the fifth positive definite gain matrix, r is the tracking error of the manipulator joint, is the estimated value of the Jacobian matrix of the robot arm, K p is the second positive definite gain matrix, e x is the tracking error of the end of the robotic arm, is the upper bound of interference, and sign() is the sign function.

[0112] Furthermore, yes The adaptive update law of the estimated value of Follow Transformation, |||r||1 is the norm of r, γ is the adaptive law constant gain;

[0113] sign() is a sign function, when r>0, sign(r)=1; when r<0, sign(r)=-1; when r=0, sign(r)=0.

[0114] S9. Control the joints of the robotic arm according to the driving torque instructions of the joints of the robotic arm to obtain the final end motion trajectory of the robotic arm.

[0115] A specific implementation method, such as Figure 2 The schematic diagram of the scenario of the robotic arm tracking the collection fingerprint in the embodiment of the robotic arm end security control method for cultural relics fingerprint of the present invention is shown. When the robotic arm is not subject to external interference, a two-degree-of-freedom planar robotic arm is considered as the simulation object. Wherein l1 and l2 are the lengths of the two connecting rods, m1 and m2 are the masses of the two connecting rods, I1 is the moment of inertia of the first connecting rod relative to the rotating shaft, and I2 is the moment of inertia of the second connecting rod relative to the center of mass. The nominal values of the robotic arm parameters are l1=l2=0.5m, m1=m2=1kg. It is assumed that the position of the end of the robotic arm can be obtained by a visual system, an electromagnetic measurement system, a position-sensitive detector or a laser tracker. Assume that the joint angle vector of the robotic arm is q=[q1,q2] T , X=[x,y] T , then its kinematic model can be obtained as formula (8):

[0116]

[0117] Formula (9) can be used to obtain formula (10):

[0118] X(t)=f(q(t))(9)

[0119]

[0120] Where: f(·) is the nonlinear vector function from joint space to task space,

[0121] The Jacobian matrix J of the robot arm is formula (11):

[0122]

[0123] make Then we have formula (12):

[0124]

[0125] Set the desired trajectory to be tracked as formula (13):

[0126]

[0127] Obviously, the desired motion trajectory selected in this embodiment has already ruled out the possibility of singularity of the robotic arm. To carry out numerical simulation verification, the following initial condition parameters are set:

[0128] q0=[1,-2] T ,

[0129] Under the action of the adaptive controller, Figure 3 The curve diagram of the expected trajectory and the actual trajectory of the end of the manipulator in the embodiment of the method for controlling the end of the manipulator for cultural relics fingerprints shown in the present invention shows that the command trajectory and the actual trajectory of the end of the manipulator are almost identical except for a slight deviation at the beginning of the task. Figure 4 The graph of the tracking error of the end of the manipulator changing with time in the embodiment of the manipulator end security control method for cultural relics fingerprint of the present invention is shown by Figure 4 It can be seen that the tracking error of the end of the manipulator tends to 0, that is, the end position of the manipulator converges to the command value, and the dynamic response time does not exceed 10 seconds, and the steady-state error of the end trajectory does not exceed 0.002 meters. Figure 5 The graph of the tracking error of the robot arm joints changing with time in the embodiment of the robot arm end security control method for cultural relics fingerprints of the present invention is shown. Figure 5 It shows that the joint coordinate q converges to the accurate inverse position solution q c , and the dynamic response time does not exceed 10 seconds, and the steady-state error of joint trajectory tracking does not exceed 0.002 radians, which verifies the effectiveness of the algorithm in solving inverse kinematics problems. Figure 6 The graph of the real-time motion trajectory of the end of the manipulator and the final end motion trajectory of the manipulator in the embodiment of the manipulator end security control method for cultural relics fingerprint of the present invention is shown by Figure 6 It can be seen that by considering the parameter perturbations of l1+5%, l2-5%, m1+10%, and m2-10%, and adjusting the control law parameters, the stability of the controlled system can still be guaranteed and the dynamic response time still does not exceed 10 seconds, the steady-state error accuracy does not decrease, and the online estimation parameters always remain bounded. By analyzing the algorithm control parameters, the following qualitative laws can be obtained: The fifth positive definite gain matrix K d The size of mainly affects the convergence rate of r, and the second positive definite gain matrix K p And the third positive definite gain matrix K v Together they determine the tracking error e at the end of the robotic arm. xThe convergence characteristics of the fourth positive definite gain matrix K A and the first positive definite gain matrix K B The convergence rate of the kinematic and dynamic parameter estimates is then adjusted (consistent excitation conditions must be met). From a theoretical perspective, the larger the values of these parameters and the closer the initial estimates are to the true values, the better the algorithm performance. However, in practical applications, it is necessary to comprehensively consider the actuator's torque output limitations and the need to suppress dynamic oscillations. Therefore, a balance must be struck between response speed and system stability to determine the optimal parameter combination.

[0130] In order to simulate the interference that may exist in real-world scenarios when the robotic arm is subject to external interference, this embodiment adds simulated unknown but bounded interference to the dynamic model. It assumes that the system is subjected to periodic external forces (such as mechanical vibration) and adds a random Gaussian white noise term to simulate sensor noise or random environmental disturbances. The interference term is assumed to be formula (14):

[0131]

[0132] Where η i (t) is the independent i-th standard Gaussian white noise, satisfying η i (t)~N(0,1).

[0133] Obviously, for the determined part, the amplitude of the interference is bounded, that is, ≤0.3 meters in the x direction and ≤0.2 meters in the y direction. For the uncertain part, that is, Gaussian noise, although it is theoretically unbounded, in practice 99.7% of the noise values fall within the range of ±3σ, so the actual amplitude of the interference term is limited to formula (15):

[0134]

[0135] like Figure 7 The graph of the real-time motion trajectory of the end of the manipulator and the final end motion trajectory of the manipulator in the embodiment of the manipulator end security control method for cultural relics fingerprints of the present invention without interference suppression is shown by Figure 7 It can be seen that when no interference suppression is applied, there is a significant deviation between the real-time motion trajectory of the end of the manipulator and the final end motion trajectory of the manipulator, which indicates that external interference will seriously affect the tracking accuracy of the system. Figure 8 The graph of the tracking error of the end of the manipulator changing with time in the embodiment of the manipulator end safety control method for cultural relics fingerprints of the present invention without interference suppression is shown by Figure 8 It can be seen that the error roughly shows periodic ups and downs, which is directly related to the periodic component of the interference signal. Obviously, the amplitude of the trajectory tracking error exceeds the allowable range of the precision operation task. Figure 9The graph showing the real-time motion trajectory of the robotic arm end and the final motion trajectory of the robotic arm end in the embodiment of the robotic arm end safety control method for cultural relic fingerprints of the present invention under the condition of interference suppression, for comparison Figure 7 , Figure 9 shows that after adding interference suppression, the real-time motion trajectory of the robotic arm end and the final motion trajectory of the robotic arm end basically coincide except for a deviation at the beginning, indicating that the designed interference adaptive law effectively updates the estimated value of the interference upper bound and compensates for the influence of external interference. Especially during the period when periodic interference acts, the trajectory tracking accuracy is significantly improved. As Figure 10 shown in the graph of the tracking error of the robotic arm end varying with time in the embodiment of the robotic arm end safety control method for cultural relic fingerprints of the present invention under the condition of interference suppression, from Figure 10 it can be seen that the amplitude of the tracking error in the x and y directions has decreased by one order of magnitude compared with that without suppression, and there is no obvious periodic fluctuation in the error curve, indicating that the periodic component in the interference is effectively suppressed. However, compared with the case without external interference, its convergence speed is significantly reduced, and it can be further optimized by adjusting the control law parameters in the future. As Figure 11 shown in the graph of the tracking error of the robotic arm joints varying with time in the embodiment of the robotic arm end safety control method for cultural relic fingerprints of the present invention under the condition of interference suppression, from Figure 11 it can be known that the actual coordinates q of the robotic arm jitter at high frequency near its inverse position solution q c , which can be ignored in most industrial scenarios, but may cause fatigue accumulation during long-term operation. Thus, it can be obtained that under the action of external interference, the trajectory tracking performance of the robotic arm is significantly affected. After introducing the interference adaptive estimation algorithm, it can effectively suppress periodic or random interference from the outside, improve the anti-interference robustness of the robotic arm trajectory tracking control system, and provide a feasible solution for high-precision control tasks.

[0136] When the robotic arm carries an optical probe to scan planar cultural relics such as murals, the design of the scanning trajectory needs to consider scanning accuracy, integrity, efficiency, and the protection of cultural relics. The following are two suitable scanning trajectories and their simulation analyses:

[0137] Cover the entire mural surface in a way of parallel straight line back-and-forth, similar to the printing path of a printer, which can be divided into horizontal grids or vertical grids. Grid scanning scans in row / column order, is not easy to miss areas, and is convenient for later data stitching, and is very suitable for regular rectangular planar murals. A typical path of grid scanning is: starting from the upper left corner, scanning horizontally to the right and then turning back, and covering the whole area downward in turn (similar to the shape of "回"). The detail resolution can be precisely controlled by adjusting the line spacing. The smaller the spacing, the denser the point cloud or texture data.

[0138] Consider a square trajectory to simulate a raster scan. Using a segmented approach, assume the square parameters are L = 0.4, x0 = 0.5, y0 = 0, where L is the side length of the square, and x0 and y0 are the x and y coordinates of the center of the square, respectively.

[0139] like Figure 12 The graph of the robot arm end tracking the square trajectory in the embodiment of the robot arm end security control method for cultural relics fingerprints of the present invention is shown. The actual trajectory of the robot arm end quickly converges to the expected trajectory, but there will be obvious deviations at the corners of the square. Figure 13 The graph of the tracking error of the robot arm joints changing with time when the robot arm end tracks a square trajectory in the embodiment of the robot arm end security control method for cultural relics fingerprints of the present invention is shown. Figure 13 As can be seen, the q1 error fluctuates around 0 most of the time, but periodic error spikes occur at specific times, both in the positive and negative directions. The q2 error base also fluctuates around 0, but periodic negative error spikes occur at specific times. These error spikes likely correspond to maneuvers such as turning at the corners of the square trajectory, requiring rapid joint adjustments and resulting in large errors. Clearly, at the corners of the square trajectory, the robot joints are subject to significant impact, causing a transient increase in friction between mechanical components. This, over time, will inevitably accelerate the wear of transmission components such as gears and bearings, shortening the robot's service life and increasing maintenance costs. To mitigate the various impact issues associated with the robot's movement at the corners of the square trajectory, this paper smoothes the square trajectory. By employing a suitable curve transition algorithm, smooth curves are introduced at the corners of the square trajectory, replacing the original sharp corners. This results in a more gradual change in direction and speed when the robot joints reach the corners, effectively reducing the impact. It can not only reduce the wear of mechanical parts and increase the service life of the robotic arm, but also improve the trajectory tracking accuracy and control stability, making the robotic arm run more smoothly and efficiently.

[0140] Add 4 arc tracks at the corners of the original 4 straight line tracks, change the original square track into a general rectangle with unequal length and width, and set the track parameters as a = 0.4, b = 0.3, r = 0.05, x c =0.5,y c =0.5, where a is the width of the rectangle, b is the height of the rectangle, r is the radius of the arc trajectory, (x c ,y c ) is the center of the rectangle.

[0141] like Figure 14The curve diagram of the smoothed square trajectory of the robot end tracking in the embodiment of the robot end safety control method for cultural relics fingerprints of the present invention is shown. Compared with the unsmoothed square trajectory, the actual trajectory can more closely follow the expected trajectory at each edge and corner. Figure 15 The graph of the tracking error of the manipulator joints over time, when the manipulator end tracked a smoothed square trajectory in an embodiment of the present invention's manipulator end safety control method for cultural relic fingerprints, shows a significant decrease in the overall deviation amplitude compared to the unsmoothed state. The deviation remains stable at a level close to 0 most of the time, and the small peaks that occur periodically are also much lower than the previous deviation values. This indicates that after smoothing, the joint angle is closer to the desired angle, the stability of the joint motion is significantly improved, and the smoothed trajectory avoids abrupt changes in motion direction, reducing inertial impact during manipulator motion and extending the service life of mechanical components.

[0142] For irregular or circular murals, a spiral scanning solution is generally used. Consider an Archimedean spiral trajectory, which is expressed as formula (16):

[0143]

[0144] Where (x0, y0) is the center offset, which translates the entire curve to the specified center. This allows the spiral trajectory to be drawn in any desired area, rather than around the origin by default. r(θ(t)) is the spiral radius parameter, which can be expressed as (17)

[0145] r(θ(t))=a+bθ(t)+csin(kθ(t))(17)

[0146] Where a is the starting radius, b is the radius added per turn, c is the perturbation amplitude, and k is the perturbation frequency. θ(t) is the nonlinear angular velocity. We let the angle θ increase at a non-uniform rate over time, and we get formula (18)

[0147] θ(t)=ωt+αsin(βt)(18)

[0148] Where ωt is uniform rotation and αsin(βt) is periodic angular velocity disturbance.

[0149] For various types of murals, we can design different parameters to obtain the appropriate Archimedean spiral trajectory, which can make the cultural relic scanning more efficient. Given a set of parameters as follows:

[0150] a=0.1, b=0.02, c=0.01, k=5, ω=0.5, α=0.1, β=2, x0=y0=0.5

[0151] like Figure 16The graph of the robotic arm's end-of-arm tracking of an Archimedean spiral trajectory, shown in an embodiment of the present invention's robotic arm end-of-arm security control method for artifact fingerprints, shows that, with the exception of a slight deviation in tracking at the spiral's center, the actual trajectory converges well to the desired trajectory at all other locations. Compared to raster scanning, spiral scanning avoids impacts at corners and reduces jitter in the joint space, helping to extend the robotic arm's lifespan and improve scanning efficiency.

[0152] like Figure 19 The system block diagram of an embodiment of a robot arm end safety control system for cultural relic fingerprints of the present invention is shown. The present invention provides a robot arm end safety control system for cultural relic fingerprints. The system is applied to a robot arm end safety control method for cultural relic fingerprints. The system includes: a first acquisition module, a second acquisition module, a first calculation module, a second calculation module, a kinematic control module, a third calculation module, a fourth calculation module, a dynamic control module and a trajectory output module. Specifically,

[0153] The first acquisition module is used to obtain the expected motion trajectory and expected motion speed according to the cultural relic fingerprint;

[0154] A second acquisition module is configured to obtain a real-time motion trajectory and a real-time motion speed of the end of the robotic arm by measuring the end trajectory of the robotic arm according to the robotic arm;

[0155] A first calculation module is used to obtain an actual trajectory and an actual speed of the robotic arm joint according to the real-time motion trajectory and the real-time motion speed of the robotic arm end;

[0156] A second calculation module is used to obtain a tracking error of the end of the robotic arm according to the expected motion trajectory and the real-time motion trajectory of the end of the robotic arm;

[0157] a kinematic control module, configured to obtain, through a kinematic model, an estimated value of a reference trajectory of the manipulator joint, a reference velocity of the manipulator joint, and a Jacobian matrix of the manipulator according to the desired motion trajectory, the desired motion velocity, the real-time motion trajectory of the manipulator end, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, and the tracking error of the manipulator end;

[0158] a third calculation module, configured to obtain a tracking error of the manipulator joint according to a reference speed of the manipulator joint and an actual speed of the manipulator joint;

[0159] a fourth calculation module, configured to obtain an adaptive update law for an estimated value of an inertial parameter vector according to a tracking error of the joint of the manipulator;

[0160] a dynamics control module, configured to obtain a driving torque command for the joint of the manipulator arm through a dynamics model based on a reference velocity of the joint of the manipulator arm, an estimated value of the Jacobian matrix of the manipulator arm, an actual trajectory of the joint of the manipulator arm, an actual velocity of the joint of the manipulator arm, a tracking error of the joint of the manipulator arm, a tracking error of the end of the manipulator arm, and an adaptive update law of an estimated value of the inertial parameter vector;

[0161] The trajectory output module is used to control the joints of the robotic arm according to the driving torque instructions of the robotic arm joints to obtain the final end motion trajectory of the robotic arm.

[0162] The present invention provides a method and system for controlling the end of a robotic arm safely for fingerprints of cultural relics. The invention targets the task of controlling the trajectory of the end of the robotic arm on the surface of cultural relics. Firstly, a kinematic model and a dynamic model of the robotic arm are established to cope with the uncertainty of the model. Secondly, an adaptive control algorithm based on the kinematic model and the dynamic model is designed, which eliminates the need to solve the inverse of the inertia matrix and measure the angular acceleration, and solves the uncertainty problem of the kinematic and dynamic parameters of the robotic arm. Finally, a globally asymptotically stable trajectory tracking control law is derived to obtain the driving torque command of the robotic arm joint, thereby ensuring that the optical probe carried by the end of the robotic arm stably tracks the desired trajectory of the cultural relic surface, and ensuring that the robotic arm can complete the task of tracking the trajectory for extracting and identifying cultural relic fingerprints under complex working conditions.

[0163] It will be appreciated that the present invention is described by way of the above embodiments and should not be construed as limiting the embodiments of the present invention and the scope of the present invention. It will be appreciated by those skilled in the art that various changes or equivalent replacements may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application fall within the scope protected by the present invention.

Claims

1. A method for controlling the end-of-arm security of cultural relics fingerprints, characterized in that: The method comprises: S1. Obtain the expected motion trajectory and expected motion speed based on the cultural relic fingerprint; S2. According to the robotic arm, by measuring the end trajectory of the robotic arm, obtain the real-time motion trajectory and real-time motion speed of the end of the robotic arm; S3, obtaining the actual trajectory and actual speed of the robotic arm joint according to the real-time motion trajectory and real-time motion speed of the robotic arm end; S4. Obtaining a tracking error of the end of the robotic arm according to the desired motion trajectory and the real-time motion trajectory of the end of the robotic arm; S5. Obtaining estimated values of a manipulator joint reference trajectory, a manipulator joint reference velocity, and a manipulator Jacobian matrix through a kinematic model based on the desired motion trajectory, the desired motion velocity, the real-time motion trajectory of the manipulator end, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, and the tracking error of the manipulator end; S6. Obtaining a tracking error of the robotic arm joint according to the robotic arm joint reference speed and the actual speed of the robotic arm joint; S7. Obtaining an adaptive update law for an estimated value of an inertial parameter vector according to the tracking error of the manipulator joint; S8. Obtaining a driving torque command for the manipulator joint through a dynamic model according to the manipulator joint reference velocity, the estimated value of the manipulator Jacobian matrix, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the tracking error of the manipulator end, and the estimated value of the inertia parameter vector; S9. Control the joints of the robotic arm according to the driving torque instructions of the joints of the robotic arm to obtain the final end motion trajectory of the robotic arm.

2. The method for controlling the end-of-arm security of a cultural relic fingerprint according to claim 1 is characterized in that: In the step S4, the tracking error of the end of the manipulator is obtained according to the expected motion trajectory and the real-time motion trajectory of the end of the manipulator, including: obtaining the tracking error of the end of the manipulator by formula (1): e x =X c (t)-X(t) (1) Where: e x is the tracking error of the end of the robot arm, X c (t) is the expected motion trajectory, and X(t) is the real-time motion trajectory of the end of the robotic arm.

3. The method for controlling the end-of-arm security of a cultural relic fingerprint according to claim 1 is characterized in that: In S5, based on the expected motion trajectory, the expected motion speed, the real-time motion trajectory of the end of the manipulator, the actual trajectory of the manipulator joint, the actual speed of the manipulator joint and the tracking error of the end of the manipulator, an estimated value of the manipulator joint reference trajectory, the manipulator joint reference speed and the manipulator Jacobian matrix is obtained through a kinematic model, including: S51. According to the tracking error of the end of the manipulator, the adaptive update law of the kinematic parameter vector estimation value is obtained by formula (2). Where: is the adaptive update law for the estimated value of the kinematic parameter vector, K B is the first positive definite gain matrix, Y K is the first linear regression matrix, q r is the reference trajectory of the robot arm joint, is the reference speed of the robot joint, K p is the second positive definite gain matrix, e x is the tracking error of the end of the robotic arm; S52, according to the actual trajectory of the manipulator joint, the actual speed of the manipulator joint and the adaptive update law of the estimated value of the kinematic parameter vector, obtain the estimated value of the manipulator Jacobian matrix through formula (3), Where: is the estimated value of the Jacobian matrix of the robot arm, q is the actual trajectory of the robot arm joint, is the actual speed of the robot arm joint; S53, according to the expected motion trajectory, the expected motion speed, the real-time motion trajectory of the end of the manipulator and the estimated value of the Jacobian matrix of the manipulator, obtain the reference speed of the manipulator joint through formula (4), Where: K v is the third positive definite gain matrix, X c (t) is the desired motion trajectory, X(t) is the real-time motion trajectory of the end of the robot arm, is the expected movement speed; S54 , obtaining a reference trajectory of the manipulator joint by integrating the reference velocity of the manipulator joint.

4. The method for controlling the end-of-arm security of a cultural relic fingerprint according to claim 1 is characterized in that: In the step S6, the tracking error of the manipulator joint is obtained according to the reference speed of the manipulator joint and the actual speed of the manipulator joint, including: obtaining the tracking error of the manipulator joint by formula (5): Where: r is the tracking error of the robot arm joint, is the reference speed of the robot joint, is the actual velocity of the robot arm joint.

5. The method for controlling the end-of-arm security of a cultural relic fingerprint according to claim 1 is characterized in that: In the step S7, the adaptive update law of the estimated value of the inertial parameter vector is obtained according to the tracking error of the manipulator joint, including: obtaining the adaptive update law of the estimated value of the inertial parameter vector by formula (6), Where: is the adaptive update law of the estimated inertial parameter vector, K A is the fourth positive definite gain matrix, Y is the second linear regression matrix, and r is the tracking error of the robotic arm joint.

6. The method for controlling the end-of-arm security of a cultural relic fingerprint according to claim 1, characterized in that: In S8, the driving torque command of the manipulator joint is obtained through a dynamic model according to the manipulator joint reference velocity, the estimated value of the manipulator Jacobian matrix, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the tracking error of the manipulator end, and the adaptive update law of the estimated value of the inertia parameter vector, including: S81. Obtain an estimated value of a reference acceleration of the manipulator joint by taking a derivative based on the manipulator joint reference velocity; S82, obtaining an estimated value of the inertia parameter vector by integration according to the adaptive update law of the estimated value of the inertia parameter vector; S83, according to the estimated value of the reference acceleration of the manipulator joint, the reference velocity of the manipulator joint, the estimated value of the manipulator Jacobian matrix, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the real-time motion trajectory of the manipulator end and the estimated value of the inertia parameter vector, obtain the driving torque instruction of the manipulator joint through formula (7), Where: τ is the driving torque command of the manipulator joint, Y is the second linear regression matrix, q is the actual trajectory of the manipulator joint, is the actual speed of the robot arm joint, is the reference speed of the robot joint, is the estimated value of the reference acceleration of the manipulator joint, is the estimated value of the inertial parameter vector, K d is the fifth positive definite gain matrix, r is the tracking error of the manipulator joint, is the estimated value of the Jacobian matrix of the robot arm, K p is the second positive definite gain matrix, e x is the tracking error of the end of the robotic arm, is the upper bound of interference, and sign() is the sign function.

7. A robot arm end safety control system for cultural relic fingerprints, used to implement the robot arm end safety control method for cultural relic fingerprints according to any one of claims 1 to 6, characterized in that: The system comprises: The first acquisition module is used to obtain the expected motion trajectory and expected motion speed according to the cultural relic fingerprint; A second acquisition module is configured to obtain a real-time motion trajectory and a real-time motion speed of the end of the robotic arm by measuring the end trajectory of the robotic arm according to the robotic arm; A first calculation module is used to obtain an actual trajectory and an actual speed of the robotic arm joint according to the real-time motion trajectory and the real-time motion speed of the robotic arm end; A second calculation module is used to obtain a tracking error of the end of the robotic arm according to the expected motion trajectory and the real-time motion trajectory of the end of the robotic arm; a kinematic control module, configured to obtain, through a kinematic model, an estimated value of a reference trajectory of the manipulator joint, a reference velocity of the manipulator joint, and a Jacobian matrix of the manipulator according to the desired motion trajectory, the desired motion velocity, the real-time motion trajectory of the manipulator end, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, and the tracking error of the manipulator end; a third calculation module, configured to obtain a tracking error of the robotic arm joint according to the robotic arm joint reference velocity and the actual velocity of the robotic arm joint; a fourth calculation module, configured to obtain an adaptive update law for an estimated value of an inertial parameter vector according to a tracking error of the manipulator joint; a dynamics control module, configured to obtain a driving torque command for the manipulator joint through a dynamics model based on the manipulator joint reference velocity, the estimated value of the manipulator Jacobian matrix, the actual trajectory of the manipulator joint, the actual velocity of the manipulator joint, the tracking error of the manipulator joint, the tracking error of the manipulator end, and the estimated value of the inertia parameter vector; The trajectory output module is used to control the joints of the robotic arm according to the driving torque instructions of the joints of the robotic arm to obtain the final end motion trajectory of the robotic arm.

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